Question: Expand and combine like terms. $(3c^4-5c^6)^2=$
Explanation: We can expand this expression using the "perfect square" pattern (where $P$ and $Q$ can be any monomial): $(P+Q)^2=P^2+2PQ+Q^2$ Since we have a minus sign, let's rewrite the binomial as a sum where the second term is negative, then use the pattern. $\begin{aligned} &\phantom{=}\left(3c^4-5c^6\right)^2 \\\\ &=\left(3c^4+\left(-5c^6\right)\right)^2 \\\\ &=(3c^4)^2+2(3c^4)(-5c^6)+(-5c^6)^2 \\\\ &=9c^8-30c^{10}+25c^{12} \\\\ &=25c^{12}-30c^{10}+9c^8 \end{aligned}$